Blender animatons not working properly in unity 3d
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Your issue could come from several things. But considering you're just starting and didn't provided enough informations to let us work fast and precisely, I would start with the more classic issues. You will have to check through, I'll try to be clear and concise.

1) Location / Rotation / Scale not initialized / applied.
If you made your rig (and so on) while your object were not placed nicely, were rotated or had a scale different of 1 (or wore, not the same scale on each axis), it will cause troubles. Always check that when done modeling, before doing anything else (including rigging).
Solution : Use the "Apply transforms" menu (ShiftA) to apply the current object's state (be aware that applying location basically means to set the object's origin to the scene's center, it's not always what you want).

2) Bad origin placement
If your object's don't have their origin at the same place, they can't possibly be imported in the same place in another software.
Solutions: Make their origins be in the same place (i.e. : scene's center)(you can use the apply location with ShiftA, or manage the origin with Ctrl Alt Shift C, or use a parent (the armature is a parent, you can also use an empty object which you set as parent of everything else and select last before exporting so that he is used as the selection's origin).

3) Skinning/weights issues
As mentioned above, it might be some issues with how you assigned your meshes to your armature. Make sure you assigned those meshes to at least one of the bones.
Solution: Use weight paint for that, it will show you the weights with colors. If its missing, either paint, or use the edit mode to select the mesh parts you want to assign, and use those widgets to do so :



Hope it helped.